feat(web): integrate Better Auth with sign-in/sign-up pages

Web app integration:
- /api/auth/[...all] route exposes Better Auth handler
- src/lib/auth.ts: server helper getServerSession() reading cookies via headers()
- src/lib/auth-client.ts: browser auth client built on shared makeAuthClient
- (auth) route group with sign-in and sign-up pages, both with email+password
  form and "Continua con Google" button (Google flow active when env is set)
- Home page becomes async, shows signed-in user name with sign-out button or
  routes to sign-up/sign-in CTAs
- Italian copy in messages/it.json under Auth.SignIn / Auth.SignUp
- transpilePackages includes @ketopath/auth
- .env.example: BETTER_AUTH_SECRET, BETTER_AUTH_URL, DATABASE_URL, Google placeholders

Build tooling:
- Drop .js extensions from internal package imports so Next webpack can
  transpile them; switch packages/db tsconfig from NodeNext to Bundler
  resolution to keep TS happy (same as packages/auth)

Verified end-to-end via browser:
- /sign-up creates user (Postgres rows in users + accounts), session cookie set,
  redirect to / shows "Accesso effettuato come Mario Test"
- /sign-out clears session, page falls back to anonymous CTAs
- /sign-in with the same credentials restores session

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/app/[locale]/(auth)/sign-in/page.tsx

@@ -0,0 +1,19 @@
+import { useTranslations } from 'next-intl';
+import { setRequestLocale } from 'next-intl/server';
+
+import { SignInForm } from './sign-in-form';
+
+export default function SignInPage({ params: { locale } }: { params: { locale: string } }) {
+  setRequestLocale(locale);
+  const t = useTranslations('Auth.SignIn');
+
+  return (
+    <main className="mx-auto flex min-h-screen max-w-md flex-col justify-center gap-8 px-6 py-16">
+      <header className="space-y-2">
+        <h1 className="text-3xl font-bold tracking-tight">{t('title')}</h1>
+        <p className="text-sm text-slate-600">{t('subtitle')}</p>
+      </header>
+      <SignInForm />
+    </main>
+  );
+}

apps/web/src/app/[locale]/(auth)/sign-in/sign-in-form.tsx

@@ -0,0 +1,113 @@
+'use client';
+
+import Link from 'next/link';
+import { useRouter } from 'next/navigation';
+import { useTranslations } from 'next-intl';
+import { useState, type FormEvent } from 'react';
+
+import { authClient } from '@/lib/auth-client';
+
+export function SignInForm() {
+  const t = useTranslations('Auth.SignIn');
+  const router = useRouter();
+  const [email, setEmail] = useState('');
+  const [password, setPassword] = useState('');
+  const [error, setError] = useState<string | null>(null);
+  const [pending, setPending] = useState(false);
+
+  async function handleSubmit(event: FormEvent<HTMLFormElement>) {
+    event.preventDefault();
+    setError(null);
+    setPending(true);
+
+    const { error: signInError } = await authClient.signIn.email({ email, password });
+
+    if (signInError) {
+      setError(signInError.message ?? t('error'));
+      setPending(false);
+      return;
+    }
+
+    router.push('/');
+    router.refresh();
+  }
+
+  async function handleGoogle() {
+    setError(null);
+    const { error: googleError } = await authClient.signIn.social({
+      provider: 'google',
+      callbackURL: '/',
+    });
+    if (googleError) {
+      setError(googleError.message ?? t('error'));
+    }
+  }
+
+  return (
+    <div className="space-y-6">
+      <form onSubmit={handleSubmit} className="space-y-4" noValidate>
+        <label className="block space-y-1">
+          <span className="text-sm font-medium text-slate-700">{t('emailLabel')}</span>
+          <input
+            type="email"
+            required
+            autoComplete="email"
+            value={email}
+            onChange={(e) => setEmail(e.target.value)}
+            className="w-full rounded-md border border-slate-300 px-3 py-2 text-sm shadow-sm focus:border-emerald-500 focus:outline-none focus:ring-1 focus:ring-emerald-500"
+          />
+        </label>
+        <label className="block space-y-1">
+          <span className="text-sm font-medium text-slate-700">{t('passwordLabel')}</span>
+          <input
+            type="password"
+            required
+            autoComplete="current-password"
+            minLength={8}
+            value={password}
+            onChange={(e) => setPassword(e.target.value)}
+            className="w-full rounded-md border border-slate-300 px-3 py-2 text-sm shadow-sm focus:border-emerald-500 focus:outline-none focus:ring-1 focus:ring-emerald-500"
+          />
+        </label>
+        {error ? (
+          <p role="alert" className="text-sm text-red-600">
+            {error}
+          </p>
+        ) : null}
+        <button
+          type="submit"
+          disabled={pending}
+          className="w-full rounded-md bg-emerald-600 px-5 py-2.5 text-sm font-medium text-white shadow-sm hover:bg-emerald-700 disabled:opacity-60"
+        >
+          {pending ? t('submitting') : t('submit')}
+        </button>
+      </form>
+      <div className="relative">
+        <div className="absolute inset-0 flex items-center">
+          <div className="w-full border-t border-slate-200" />
+        </div>
+        <div className="relative flex justify-center">
+          <span className="bg-white px-2 text-xs uppercase tracking-wider text-slate-500">
+            {t('or')}
+          </span>
+        </div>
+      </div>
+      <button
+        type="button"
+        onClick={handleGoogle}
+        className="w-full rounded-md border border-slate-300 bg-white px-5 py-2.5 text-sm font-medium text-slate-700 shadow-sm hover:bg-slate-50"
+      >
+        {t('google')}
+      </button>
+      <p className="text-center text-sm text-slate-600">
+        {t.rich('noAccount', {
+          link: (chunks) => (
+            <Link href="/sign-up" className="font-medium text-emerald-700 hover:underline">
+              {chunks}
+            </Link>
+          ),
+        })}
+      </p>
+    </div>
+  );
+}

apps/web/src/app/[locale]/(auth)/sign-up/page.tsx

@@ -0,0 +1,20 @@
+import { useTranslations } from 'next-intl';
+import { setRequestLocale } from 'next-intl/server';
+
+import { SignUpForm } from './sign-up-form';
+
+export default function SignUpPage({ params: { locale } }: { params: { locale: string } }) {
+  setRequestLocale(locale);
+  const t = useTranslations('Auth.SignUp');
+
+  return (
+    <main className="mx-auto flex min-h-screen max-w-md flex-col justify-center gap-8 px-6 py-16">
+      <header className="space-y-2">
+        <h1 className="text-3xl font-bold tracking-tight">{t('title')}</h1>
+        <p className="text-sm text-slate-600">{t('subtitle')}</p>
+      </header>
+      <SignUpForm />
+      <p className="text-xs text-slate-500">{t('disclaimer')}</p>
+    </main>
+  );
+}

apps/web/src/app/[locale]/(auth)/sign-up/sign-up-form.tsx

@@ -0,0 +1,126 @@
+'use client';
+
+import Link from 'next/link';
+import { useRouter } from 'next/navigation';
+import { useTranslations } from 'next-intl';
+import { useState, type FormEvent } from 'react';
+
+import { authClient } from '@/lib/auth-client';
+
+export function SignUpForm() {
+  const t = useTranslations('Auth.SignUp');
+  const router = useRouter();
+  const [name, setName] = useState('');
+  const [email, setEmail] = useState('');
+  const [password, setPassword] = useState('');
+  const [error, setError] = useState<string | null>(null);
+  const [pending, setPending] = useState(false);
+
+  async function handleSubmit(event: FormEvent<HTMLFormElement>) {
+    event.preventDefault();
+    setError(null);
+    setPending(true);
+
+    const { error: signUpError } = await authClient.signUp.email({ email, password, name });
+
+    if (signUpError) {
+      setError(signUpError.message ?? t('error'));
+      setPending(false);
+      return;
+    }
+
+    router.push('/');
+    router.refresh();
+  }
+
+  async function handleGoogle() {
+    setError(null);
+    const { error: googleError } = await authClient.signIn.social({
+      provider: 'google',
+      callbackURL: '/',
+    });
+    if (googleError) {
+      setError(googleError.message ?? t('error'));
+    }
+  }
+
+  return (
+    <div className="space-y-6">
+      <form onSubmit={handleSubmit} className="space-y-4" noValidate>
+        <label className="block space-y-1">
+          <span className="text-sm font-medium text-slate-700">{t('nameLabel')}</span>
+          <input
+            type="text"
+            required
+            autoComplete="name"
+            value={name}
+            onChange={(e) => setName(e.target.value)}
+            className="w-full rounded-md border border-slate-300 px-3 py-2 text-sm shadow-sm focus:border-emerald-500 focus:outline-none focus:ring-1 focus:ring-emerald-500"
+          />
+        </label>
+        <label className="block space-y-1">
+          <span className="text-sm font-medium text-slate-700">{t('emailLabel')}</span>
+          <input
+            type="email"
+            required
+            autoComplete="email"
+            value={email}
+            onChange={(e) => setEmail(e.target.value)}
+            className="w-full rounded-md border border-slate-300 px-3 py-2 text-sm shadow-sm focus:border-emerald-500 focus:outline-none focus:ring-1 focus:ring-emerald-500"
+          />
+        </label>
+        <label className="block space-y-1">
+          <span className="text-sm font-medium text-slate-700">{t('passwordLabel')}</span>
+          <input
+            type="password"
+            required
+            autoComplete="new-password"
+            minLength={8}
+            value={password}
+            onChange={(e) => setPassword(e.target.value)}
+            className="w-full rounded-md border border-slate-300 px-3 py-2 text-sm shadow-sm focus:border-emerald-500 focus:outline-none focus:ring-1 focus:ring-emerald-500"
+          />
+          <span className="block text-xs text-slate-500">{t('passwordHint')}</span>
+        </label>
+        {error ? (
+          <p role="alert" className="text-sm text-red-600">
+            {error}
+          </p>
+        ) : null}
+        <button
+          type="submit"
+          disabled={pending}
+          className="w-full rounded-md bg-emerald-600 px-5 py-2.5 text-sm font-medium text-white shadow-sm hover:bg-emerald-700 disabled:opacity-60"
+        >
+          {pending ? t('submitting') : t('submit')}
+        </button>
+      </form>
+      <div className="relative">
+        <div className="absolute inset-0 flex items-center">
+          <div className="w-full border-t border-slate-200" />
+        </div>
+        <div className="relative flex justify-center">
+          <span className="bg-white px-2 text-xs uppercase tracking-wider text-slate-500">
+            {t('or')}
+          </span>
+        </div>
+      </div>
+      <button
+        type="button"
+        onClick={handleGoogle}
+        className="w-full rounded-md border border-slate-300 bg-white px-5 py-2.5 text-sm font-medium text-slate-700 shadow-sm hover:bg-slate-50"
+      >
+        {t('google')}
+      </button>
+      <p className="text-center text-sm text-slate-600">
+        {t.rich('haveAccount', {
+          link: (chunks) => (
+            <Link href="/sign-in" className="font-medium text-emerald-700 hover:underline">
+              {chunks}
+            </Link>
+          ),
+        })}
+      </p>
+    </div>
+  );
+}

apps/web/src/app/[locale]/page.tsx

@@ -1,28 +1,46 @@
+import Link from 'next/link';
 import { useTranslations } from 'next-intl';
 import { setRequestLocale } from 'next-intl/server';
 
-export default function HomePage({ params: { locale } }: { params: { locale: string } }) {
+import { getServerSession } from '@/lib/auth';
+
+import { SignOutButton } from './sign-out-button';
+
+export default async function HomePage({ params: { locale } }: { params: { locale: string } }) {
   setRequestLocale(locale);
+  const session = await getServerSession();
+
+  return <HomeContent userName={session?.user?.name ?? session?.user?.email ?? null} />;
+}
+
+function HomeContent({ userName }: { userName: string | null }) {
   const t = useTranslations('Home');
 
   return (
     <main className="mx-auto flex min-h-screen max-w-3xl flex-col items-start justify-center gap-6 px-6 py-16">
       <h1 className="text-4xl font-bold tracking-tight sm:text-5xl">{t('title')}</h1>
       <p className="text-lg text-slate-600">{t('tagline')}</p>
-      <div className="flex flex-wrap gap-3">
-        <button
-          type="button"
-          className="rounded-md bg-emerald-600 px-5 py-2.5 text-sm font-medium text-white shadow-sm hover:bg-emerald-700 focus:outline-none focus-visible:ring-2 focus-visible:ring-emerald-500"
-        >
-          {t('ctaPrimary')}
-        </button>
-        <button
-          type="button"
-          className="rounded-md border border-slate-300 bg-white px-5 py-2.5 text-sm font-medium text-slate-700 shadow-sm hover:bg-slate-50 focus:outline-none focus-visible:ring-2 focus-visible:ring-slate-400"
-        >
-          {t('ctaSecondary')}
-        </button>
-      </div>
+      {userName ? (
+        <div className="flex flex-wrap items-center gap-3">
+          <span className="text-sm text-slate-700">{t('signedInAs', { name: userName })}</span>
+          <SignOutButton label={t('signOut')} />
+        </div>
+      ) : (
+        <div className="flex flex-wrap gap-3">
+          <Link
+            href="/sign-up"
+            className="rounded-md bg-emerald-600 px-5 py-2.5 text-sm font-medium text-white shadow-sm hover:bg-emerald-700 focus:outline-none focus-visible:ring-2 focus-visible:ring-emerald-500"
+          >
+            {t('ctaPrimary')}
+          </Link>
+          <Link
+            href="/sign-in"
+            className="rounded-md border border-slate-300 bg-white px-5 py-2.5 text-sm font-medium text-slate-700 shadow-sm hover:bg-slate-50 focus:outline-none focus-visible:ring-2 focus-visible:ring-slate-400"
+          >
+            {t('ctaSecondary')}
+          </Link>
+        </div>
+      )}
       <p className="mt-8 text-xs text-slate-500">{t('disclaimer')}</p>
     </main>
   );

apps/web/src/app/[locale]/sign-out-button.tsx

@@ -0,0 +1,29 @@
+'use client';
+
+import { useRouter } from 'next/navigation';
+import { useState } from 'react';
+
+import { authClient } from '@/lib/auth-client';
+
+export function SignOutButton({ label }: { label: string }) {
+  const router = useRouter();
+  const [pending, setPending] = useState(false);
+
+  async function handleClick() {
+    setPending(true);
+    await authClient.signOut();
+    router.push('/');
+    router.refresh();
+  }
+
+  return (
+    <button
+      type="button"
+      onClick={handleClick}
+      disabled={pending}
+      className="rounded-md border border-slate-300 bg-white px-3 py-1.5 text-xs font-medium text-slate-700 shadow-sm hover:bg-slate-50 disabled:opacity-60"
+    >
+      {label}
+    </button>
+  );
+}